We report resonant x-ray scattering measurements on a single crystal of the orbitally degenerate triangular metallic antiferromagnet 2H-AgNiO2 to probe the spontaneous transition to a triple-cell superstructure at temperatures below T-S = 365 K. We observe a strong resonant enhancement of the supercell reflections through the Ni K edge. The empirically extracted K-edge shift between the crystallographically distinct Ni sites of 2.5(3) eV is much larger than the value expected from the shift in final states, and implies a core-level shift of similar to 1 eV, thus providing direct evidence for the onset of spontaneous honeycomb charge order in the triangular Ni layers. We also provide band-structure calculations that explain quantitatively the observed edge shifts in terms of changes in the Ni electronic energy levels due to charge order and hybridization with the surrounding oxygens.